Abstract
In this paper, we present Padé approximations of some functions involving complete elliptic integrals of the first kind
K
(
x
)
, and motivated by these approximations we also present the following double inequality:
1
−
x
2
1
−
x
2
+
x
4
62
<
2
e
2
π
K
(
x
)
−
1
(
1
+
1
1
−
x
2
)
<
1
−
96
100
x
2
1
−
96
100
x
2
+
x
4
64
,
x
∈
(
0
,
1
)
.
Our results have superiority over some new recent results.